Jigsaw puzzles have been a popular diversion for hundreds of years. A typical two-dimensional jigsaw puzzle comprises a flat sheet of material (e.g., cardboard), typically with a picture printed on the front, cut into pieces to be reassembled. Methods for determining the pattern to cut the sheet can be fairly simple, for example, the sheet of material can nominally be cut along a grid pattern. The grid pattern is typically modified to make the pieces distinct from one another (e.g., by pulling grid points away from their original locations), and connections are added (e.g., connections formed from plugs protruding out from a piece and complementary holes entering into a piece). A three-dimensional jigsaw puzzle can be considerably more complicated to design. A three-dimensional shape can be built up from flat pieces connected together at angles to one another; however, this process causes the finished three-dimensional shape to depend on the shapes of the pieces, unlike a two-dimensional puzzle. Determining the shapes of the pieces to create a desired three-dimensional volume can be very complicated. Additionally, in order to join the pieces at angles to one another, the pieces must bend at the joints. Fabricating the pieces such that they bend at the joints, by a particular amount, in a durable and repeatable way, can be difficult and expensive.